On Data Augmentation for Models Involving Reciprocal Gamma Functions

In this article, we introduce a new and efficient data augmentation approach to the posterior inference of models with shape parameters when reciprocal gamma function appears in full conditional densities. Our is approximate densities by using Gauss’s multiplication formula Stirling’s for function, where approximation error can be made arbitrarily small. We use techniques construct Gibbs Metropolis–Hastings algorithms variety that involve distribution, Student’s t-distribution, Dirichlet negative binomial Wishart distribution. The proposed sampling method numerically demonstrated through simulation studies. Supplementary materials article are available online.